Mathematical Sciences: A Research Initiation for Undergraduates Via Differential Equations, Difference Equations and Chaos

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Support for five undergraduate students engaged in mathematical research will be supported by this Research Experiences for Undergraduates award. The students will perform numerical analysis, investigate difference equations and engage in studies of chaos as modeled by the process of iteration of continuous maps. The main focus of the research will be on the oscillatory behavior of difference equations and the role of symmetry in chaotic planar dynamics. The program will run for eight weeks. Faculty from the University of Houston (UH) will also participate in the program. This will be done in several ways. First, the University of Houston will provide a faculty member to work with the students on problems of differential equations and chaos. A second faculty member from Furman University will teach the necessary introductory material on chaos. Her salary will be paid by UH. Students will spend each Friday morning at UH visiting laboratories such as the Dynamics Laboratory and laboratories in the Departments of Physics, Mechanical Engineering and Chemical Engineering where chaotic dynamics is observed experimentally. A portion of the program's research component will involve transferring of software, which has been developed at UH to study iterates of mappings and dynamics with symmetry, to the PC environment which is being developed at TSU. A study of these mappings can be made at many levels, from proving theorems in group representations to parameter exploration in quadratic maps. In addition, UH will provide funds for three REU students to work with the five from TSU. An active program of colloquium lectures, counselling and social events is also planned. Students will be encouraged to present the results of their work at the annual meeting of the Association of Minority Professors.